CN111400911A - GNSS deformation information identification and early warning method based on EWMA control chart - Google Patents
GNSS deformation information identification and early warning method based on EWMA control chart Download PDFInfo
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- CN111400911A CN111400911A CN202010183171.8A CN202010183171A CN111400911A CN 111400911 A CN111400911 A CN 111400911A CN 202010183171 A CN202010183171 A CN 202010183171A CN 111400911 A CN111400911 A CN 111400911A
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Abstract
The invention discloses GNSS deformation information identification and early warning based on an EWMA control chart, which comprises the following steps of (1) acquiring GNSS deformation monitoring data of a monitoring body, calculating a calculated mean value mu and a standard deviation sigma of the GNSS deformation monitoring data, (2) setting a weight parameter lambda and a control limit width L of the EWMA control chart according to the characteristics of the monitoring data, (3) constructing an offset statistic Z of the EWMA control chart from the monitoring data containing the deformation data, (4) determining a central line and upper and lower reference limits of an abnormal value identification model, and (5) comparing and judging whether the EWMA offset statistic exceeds the control limit, and defining the data exceeding the control limit as abnormal data and early warning.
Description
Technical Field
The invention relates to the early warning field of surveying and mapping deformation monitoring, in particular to a GNSS deformation information identification and early warning method based on an EWMA control chart.
Background
With the rapid development of global economy, the range of human activities is continuously expanded, high-rise buildings, large bridges and highways are continuously built, and disaster events caused by the deformation of buildings emerge endlessly. In order to guarantee the life and property safety of people, effective deformation monitoring of buildings is necessary, and the GNSS positioning technology has the advantages of real-time dynamic high precision and is widely applied to the field of deformation monitoring. And processing and analyzing the acquired deformation information of the GNSS monitoring data by adopting a certain mathematical method, and early warning in time so as to reduce the probability of disaster occurrence and reduce the influence range of the disaster occurrence.
Currently, a common method for checking and early warning GNSS monitoring data is a CUSUM control chart method, but the method has two problems: firstly, the identification result of continuous large-offset deformation information is poor, and secondly, the false alarm rate is increased along with the continuous increase of the deformation. In view of this, the EWMA control chart is provided to identify and warn GNSS disaster information, and a new GNSS deformation information identification and warning method is provided in combination with relevant features of a GNSS coordinate sequence. The method has higher identification precision on deformation information than a classic CUSUM control chart method, and the false alarm rate is greatly improved.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a GNSS deformation information identification and early warning method based on an EWMA control chart. The invention uses the EWMA control chart for the identification and early warning of GNSS deformation information for the first time, can accurately analyze the change trend and the deformation information of the monitored data, and has the advantages of better deformation information inspection capability and lower false alarm rate.
The invention adopts the following technical scheme for realizing the purpose:
a GNSS deformation information identification and early warning method based on an EWMA control chart comprises the following steps:
step 1, acquiring GNSS deformation monitoring data of a monitoring body, and calculating a calculation mean value mu and a standard deviation sigma of the GNSS deformation monitoring data;
step 2, setting a weight parameter lambda and a control limit width L of an EWMA control chart;
step 3, constructing an offset statistic Z of the EWMA control chart according to the acquired monitoring data;
step 4, determining a central line and upper and lower reference limits of the abnormal value identification model;
and 5, comparing and judging whether the EWMA deviation statistic exceeds the control limit, defining the data exceeding the control limit as abnormal data and carrying out early warning.
Preferably, the GNSS deformation information identification and early warning method based on the EWMA control chart is characterized in that in step 1, a GNSS time series for deformation monitoring of a monitored body (a structure or a building) is collected, the time series is subjected to preliminary analysis, and a mean value μ and a standard deviation σ are calculated.
Preferably, according to claim 1, the GNSS deformation information identification and early warning method based on the EWMA control chart is characterized in that in step 2, a weight parameter λ of the EMWA control chart generally has a value range of [0.05,0.25], in order to highlight the control chart inspection performance, λ has a value of 0.1, and a control limit width has a value of 3.
Preferably, the GNSS deformation information identification and early warning method based on the EWMA control map is characterized in that in step 3, the offset statistic Z of the EWMA control map is constructed.
For GNSS monitoring data x (i) observed for a long time, i ═ 1,2, …, n, n is the sample size. Offset statistic Z for EWMA control chartiIs defined as:
Zi＝λXi+(1-λ)Zi-1(1)
wherein λ is weight parameter of EWMA control chart, and belongs to [0,1 ]]In the constant, λ is 0.1; initial value Z0(i-1) is the process target value, substituted by the mean of the observed values x (i), Z0＝μ0。
Because of ZiIs a weighted average of the mean of all previous samples of the EWMA by replacing Z on the right side of the equationi-1To obtain:
Zi＝λXi+(1-λ)[λXi-1+(1-λ)Zi-2]＝λXi+λ(1-λ)Xi-1+(1-λ)2Zi-2(2)
continue to replace Z with recursioni-jJ 2,3, …, t, we get
Preferably, the GNSS deformation information identification and early warning method based on EWMA control chart is characterized in that in step 4, a center line C L and an upper reference limit UC L of an outlier identification model and a lower reference line L C L are determined.
GNSS observation data X (t) is the data with variance σ2Independent random variables of (a), the constructed EWMA statistic ZiThe variance of (c) is as follows:
therefore, statistic Z by constructing GNSS monitoring data as EWMA control chartiTogether with time (epoch), the EWMA control chart is composed, and the verification criteria of the deformation information are as follows:
CL＝μ0(6)
l is the width of the control limit when the inspection threshold is constructed, the value is generally 3, the calculation formulas of an upper reference limit UC L, a central line C L and a lower reference line L C L of an abnormal value recognition model are shown in the formula (5), the formula (6) and the formula (7), and when the constructed deviation statistic exceeds UC L or-L C L, the abnormal value recognition model is regarded as deformation information and gives an early warning.
Preferably, the GNSS deformation information identification and early warning method based on EWMA control graph according to claim 1, wherein in step 5, it is determined whether EWMA deviation statistic Z obtained in step 3 exceeds a control limit range formed by an upper reference limit UC L and a lower reference line L C L, and data exceeding the control limit is defined as abnormal data and early warning is performed
Compared with the prior art, the invention has the beneficial effects that: the invention uses the EWMA control chart for the identification and early warning of GNSS deformation information for the first time, can accurately analyze the change trend and the deformation information of the monitored data, and has the advantages of better deformation information inspection capability and lower false alarm rate.
Drawings
FIG. 1 is a flowchart illustrating a GNSS deformation information recognition and early warning method based on EWMA control chart according to a preferred embodiment of the present invention;
FIG. 2 is a sequence of raw GNSS coordinates without deformation information for use in experiments in the case of the present invention;
FIG. 3 is data for the case of the present invention with 1-4 times the standard deviation distortion information added, respectively;
FIG. 4 is the recognition result of the EWMA control chart on different standard deviation deformation data in the case of the present invention;
FIG. 5 is the recognition result of CUSUM control chart on different standard deviation deformation data in the case of the present invention;
Detailed Description
The following detailed description of the preferred embodiments of the present invention, taken in conjunction with the accompanying drawings, will make the advantages and features of the invention easier to understand by those skilled in the art, and thus will clearly and clearly define the scope of the invention.
Referring to fig. 1, an embodiment of the present invention includes:
a GNSS deformation information identification and early warning method based on an EWMA control chart comprises the following steps:
step 1, acquiring GNSS deformation monitoring data of a monitoring body, and calculating a calculation mean value mu and a standard deviation sigma of the GNSS deformation monitoring data;
step 2, setting a weight parameter lambda and a control limit width L of an EWMA control chart;
step 3, constructing an offset statistic Z of the EWMA control chart according to the acquired monitoring data;
step 4, determining a central line and upper and lower reference limits of the abnormal value identification model;
and 5, comparing and judging whether the EWMA deviation statistic exceeds the control limit, defining the data exceeding the control limit as abnormal data and carrying out early warning.
Taking the GNSS monitoring time sequence of a certain building as an example, the specific implementation steps are as follows:
in the first step, a set of GNSS monitoring data containing simulation deformation information is adopted for testing.
The original GNSS data is from a GNSS continuous tracking station on the roof of the university of Anhui Ringman, and the station is relatively stable and has no deformation sign. And intercepting a time-interval X-direction coordinate sequence (the sampling time is 1500s, the sampling interval is 1s, and the sampling frequency is 1Hz) in the station, and subtracting the data of the true value (obtained by long-time observation average) to obtain the original GNSS monitoring data, as shown in FIG. 2.
The upper offsets of 1-4 times of the standard deviation are added to the original GNSS coordinate sequence at 701-900 epochs, respectively, to form GNSS monitoring data with four sets of variant variants, as shown in FIG. 3. And analyzing the GNSS monitoring sequence containing the deformation information, and calculating the calculation mean value mu and the standard deviation sigma.
And secondly, setting a weight parameter lambda and a control limit width L of the EWMA control chart, wherein the weight parameter lambda of the EMWA control chart generally has a value range of [0.05 and 0.25], and in order to highlight the inspection performance of the control chart, the value of lambda is 0.1, and the value of the control limit width is 3.
Thirdly, according to the GNSS monitoring data containing the deformation information, constructing an offset statistic Z of the EWMA control chart, wherein the formula is as follows:
for GNSS monitoring data x (i) observed for a long time, i ═ 1,2, …, n, n is the sample size. Offset statistic Z for EWMA control chartiIs defined as:
Zi＝λXi+(1-λ)Zi-1(1)
wherein λ is weight parameter of EWMA control chart, and belongs to [0,1 ]]In the constant, λ is 0.1; initial value Z0(i-1) is the process target value, substituted by the mean of the observed values x (i), Z0＝μ0。
Because of ZiIs a weighted average of the mean of all previous samples of the EWMA by replacing Z on the right side of the equationi-1To obtain:
Zi＝λXi+(1-λ)[λXi-1+(1-λ)Zi-2]＝λXi+λ(1-λ)Xi-1+(1-λ)2Zi-2(2)
continue to replace Z with recursioni-j，j＝2,3,…,t，We obtain
Fourthly, determining a center line C L and an upper reference limit UC L and a lower reference line L C L of the abnormal value recognition model based on the EWMA control chart.
GNSS observation data X (t) is the data with variance σ2Independent random variables of (a), the constructed EWMA statistic ZiThe variance of (c) is as follows:
therefore, statistic Z by constructing GNSS monitoring data as EWMA control chartiTogether with time (epoch), the EWMA control chart is composed, and the verification criteria of the deformation information are as follows:
CL＝μ0(6)
l is the width of the control limit when the inspection threshold is constructed, the value is generally 3, the calculation formula of the upper reference limit UC L center line C L and the lower reference line L C L of the abnormal value recognition model is shown in formula (5), formula (6) and formula (7), and when the constructed deviation statistic exceeds UC L or-L C L, the abnormal value recognition model is regarded as deformation information and gives an early warning.
And fifthly, based on the steps, performing outlier inspection and analysis on the four groups of GNSS monitoring data with the deformation information added with the standard deviation of 1-4 times by adopting an EWMA control chart, as shown in FIG. 4. Abnormal value detection analysis is carried out on the four groups of GNSS monitoring data containing deformation information added with 1-4 times of standard deviation by adopting a common method CUSUM control chart, as shown in figure 5. The results obtained by both methods were analyzed as shown in tables 1 and 2.
TABLE 1 CUSUM control chart recognition results of different standard deviation deformation data
TABLE 2 EWMA control chart recognition results for different standard deviation deformation data
As shown in fig. 4 and 5 and tables 1 and 2: for the deformation information with the offset of 1-4 times of standard deviation added in 701-900 epochs, the early warning numbers of the upper offset of the CUSUM control chart are 327, 471, 492 and 518 respectively, and the early warning numbers of the lower offset are 324, 408, 427 and 438; the warning numbers of the upper offsets of the EWMA control chart are 156, 213, 215, and 267, respectively, and the warning numbers of the lower offsets are 117, 124, 123, and 367, respectively. In general, no matter the lower offset deformation data is added into the upper offset deformation information or the actual measurement data, the accuracy of the EWMA control chart detection and early warning is higher than that of the CUSUM control chart, and the result has certain reliability. When the continuous small offset deformation information below 2 times is detected and early-warned, the detection and early-warning results of the CUSUM control chart are general, and the false alarm quantity of the offset deformation information above 2 times exceeds the real range of the actually added deformation information, so the accuracy of the detection and early-warning results is low; compared with the CUSUM control chart, the deformation information detected by the EWMA control chart is mostly surrounded in the range of the added real deformation information, and the result is superior to that of the CUSUM control chart. In addition, the study does not add any under-biased deformation information to the test data, but both control map algorithms verify certain deformation data, which may be caused by gross differences in the measured data. The error alarm rates of the EWMA control chart and the CUSUM control chart are increased along with the continuous increase of the standard deviation deformation information, and as can be seen from tables 1-2 and 4-5, the EWMA control chart is greatly improved in the error alarm rate, and the error alarm rate is reduced by more than 50%. Meanwhile, aiming at the detection and early warning of the lower offset deformation information, compared with a CUSUM control chart, the EWMA control chart has a certain inhibiting effect on gross errors, so that the detection and early warning result has certain reliability and stability.
By analyzing the results, the following conclusions can be drawn:
(1) aiming at the detection and early warning of deformation information with different standard deviations, the EWMA control chart and the classic CUSUM control chart can effectively detect the deformation information.
(2) When the continuous large-offset deformation information with the standard deviation more than 2 times is detected and early-warned, the detection early-warning capability of the EWMA control chart is obviously superior to that of the CUSUM control chart, and meanwhile, the false warning rate is greatly improved
(3) Although no under-shifted deformation information was added to the test data, both control map algorithms verified certain deformation data, which may be caused by gross differences in the measured data. However, with the continuous increase of the standard deviation, the range of detected deformation information is also continuously increased, compared with the CUSUM algorithm, the EWMA control chart has a certain inhibition effect on gross errors, and the detection and early warning results have certain reliability and stability.
The invention aims to provide a GNSS deformation information identification and early warning method based on an EWMA control chart. The invention applies the EWMA control chart to the identification and early warning of GNSS deformation information for the first time, can accurately analyze the change trend and the deformation information of the monitored data, and has the advantages of better deformation information inspection capability and lower false alarm rate.
Therefore, it should be understood that any modification, equivalent replacement, decoration, improvement, etc. made by those skilled in the art within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. A GNSS deformation information identification and early warning method based on an EWMA control chart is characterized by comprising the following steps:
step 1, acquiring GNSS deformation monitoring data of a monitoring body, and calculating a calculation mean value mu and a standard deviation sigma of the GNSS deformation monitoring data;
step 2, setting a weight parameter lambda and a control limit width L of an EWMA control chart;
step 3, constructing an offset statistic Z of the EWMA control chart according to the acquired monitoring data;
step 4, determining a central line and upper and lower reference limits of the abnormal value identification model;
and 5, comparing and judging whether the EWMA deviation statistic exceeds the control limit, defining the data exceeding the control limit as abnormal data and carrying out early warning.
2. The GNSS deformation information identification and early warning method based on EWMA control chart is characterized in that in step 1, GNSS time series for deformation monitoring of a monitored body (structure or building) is collected, the time series is subjected to preliminary analysis, and the mean value mu and the standard deviation sigma are calculated.
3. The GNSS deformation information identification and early warning method based on the EWMA control chart is characterized in that in the step 2, the value range of the weight parameter lambda of the EMWA control chart is [0.05,0.25], in order to highlight the control chart inspection performance, the value of lambda is 0.1, and the value of the control limit width is 3.
4. The GNSS deformation information identification and early warning method based on the EWMA control chart, as claimed in claim 1, wherein in step 3, the offset statistic Z of the EWMA control chart is constructed.
For GNSS monitoring data x (i) observed for a long time, i ═ 1,2, …, n, n is the sample size. Offset statistic Z for EWMA control chartiIs defined as:
Zi＝λXi+(1-λ)Zi-1(1)
wherein λ is weight parameter of EWMA control chart, and belongs to [0,1 ]]In the constant, λ is 0.1; initial value Z0(i＝1) is the process target value, substituted by the mean of the observed values X (i), Z0＝μ0。
Because of ZiIs a weighted average of the mean of all previous samples of the EWMA by replacing Z on the right side of the equationi-1To obtain:
Zi＝λXi+(1-λ)[λXi-1+(1-λ)Zi-2]＝λXi+λ(1-λ)Xi-1+(1-λ)2Zi-2(2)
continue to replace Z with recursioni-jJ 2,3, …, t, we get
5. The GNSS deformation information recognition and early warning method based on EWMA control chart as claimed in claim 1, wherein in step 4, the center line C L and the upper reference limit UC L and the lower reference line L C L of the outlier recognition model are determined.
GNSS observation data X (t) is the data with variance σ2Independent random variables of (a), the constructed EWMA statistic ZiThe variance of (c) is as follows:
therefore, statistic Z by constructing GNSS monitoring data as EWMA control chartiTogether with time (epoch), the EWMA control chart is composed, and the verification criteria of the deformation information are as follows:
CL＝μ0(6)
l is the width of the control limit when the inspection threshold is constructed, the value is generally 3, the calculation formulas of an upper reference limit UC L, a central line C L and a lower reference line L C L of an abnormal value recognition model are shown in the formula (5), the formula (6) and the formula (7), and when the constructed deviation statistic exceeds UC L or-L C L, the abnormal value recognition model is regarded as deformation information and gives an early warning.
6. The GNSS deformation information identification and early warning method based on EWMA control map as claimed in claim 1, wherein in step 5, it is determined whether the EWMA offset statistic Z obtained in step 3 exceeds the control limit range formed by the upper reference limit UC L and the lower reference line L C L, and data exceeding the control limit is defined as abnormal data and early warning is performed.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN112487364A (en) * | 2020-12-10 | 2021-03-12 | 北部湾大学 | Small leakage detection method based on exponential weighted moving average algorithm |
| CN112581727A (en) * | 2020-11-16 | 2021-03-30 | 西人马联合测控（泉州）科技有限公司 | Displacement drift early warning method, device, equipment and storage medium of bridge |
| CN112734977A (en) * | 2020-12-25 | 2021-04-30 | 安徽省安泰科技股份有限公司 | Equipment risk early warning system and algorithm based on Internet of things |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN112581727A (en) * | 2020-11-16 | 2021-03-30 | 西人马联合测控（泉州）科技有限公司 | Displacement drift early warning method, device, equipment and storage medium of bridge |
| CN112581727B (en) * | 2020-11-16 | 2022-08-19 | 西人马联合测控（泉州）科技有限公司 | Bridge displacement drift early warning method, device, equipment and storage medium |
| CN112487364A (en) * | 2020-12-10 | 2021-03-12 | 北部湾大学 | Small leakage detection method based on exponential weighted moving average algorithm |
| CN112487364B (en) * | 2020-12-10 | 2022-03-11 | 北部湾大学 | Small leakage detection method based on exponential weighted moving average algorithm |
| CN112734977A (en) * | 2020-12-25 | 2021-04-30 | 安徽省安泰科技股份有限公司 | Equipment risk early warning system and algorithm based on Internet of things |
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